Gauging quantum states: from global to local symmetries in many-body systems

TL;DR

This paper introduces a method to convert global symmetries into local gauge symmetries at the quantum state level, enabling the study of gauge theories and phase diagrams in many-body systems using PEPS formalism.

Contribution

It develops a state-level gauging procedure, constructs a compatible operator gauging map, and demonstrates the approach with PEPS and a Z2 gauge theory example.

Findings

Gauged PEPS can exhibit topological order.

The parent Hamiltonian closely relates to the Kogut-Susskind Hamiltonian.

The scheme allows probing phase diagrams of gauge theories.

Abstract

We present an operational procedure to transform global symmetries into local symmetries at the level of individual quantum states, as opposed to typical gauging prescriptions for Hamiltonians or Lagrangians. We then construct a compatible gauging map for operators, which preserves locality and reproduces the minimal coupling scheme for simple operators. By combining this construction with the formalism of projected entangled-pair states (PEPS), we can show that an injective PEPS for the matter fields is gauged into a G-injective PEPS for the combined gauge-matter system, which potentially has topological order. We derive the corresponding parent Hamiltonian, which is a frustration free gauge theory Hamiltonian closely related to the Kogut-Susskind Hamiltonian at zero coupling constant. We can then introduce gauge dynamics at finite values of the coupling constant by applying a local filtering operation. This scheme results in a low-parameter family of gauge invariant states of which we can accurately probe the phase diagram, as we illustrate by studying a Z2 gauge theory with Higgs matter.